Problem: Simplify the following expression: $z = \dfrac{15a - 30}{12a - 3}$ You can assume $a \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $15a - 30 = (3\cdot5 \cdot a) - (2\cdot3\cdot5)$ The denominator can be factored: $12a - 3 = (2\cdot2\cdot3 \cdot a) - (3)$ The greatest common factor of all the terms is $3$ Factoring out $3$ gives us: $z = \dfrac{(3)(5a - 10)}{(3)(4a - 1)}$ Dividing both the numerator and denominator by $3$ gives: $z = \dfrac{5a - 10}{4a - 1}$